Accurate analysis of earth penetration by a non-normal impact of projectile is crucial for the design of earth penetration system. This phenomenon has been studied in details in an existing Simulia Technology Brief on “Earth Penetration Simulation using Coupled Eulerian-Lagrangian (CEL) Analysis”. In comparison with CEL, Smoothed Particle Hydrodynamics (SPH) offers higher modeling simplicity.
A study is carried out to understand the effect of various SPH control parameters on the results of simulation. Following parameters are observed to predominantly affect result accuracy of SPH simulation:
- Mesh sensitivity:
- With a very fine mesh, projectile does not completely penetrates the earth block
- With a very coarse mesh, projectile passes through the earth block
- Mesh with moderate size provides appropriate results
- Uniform mesh pattern works better than non-uniform mesh pattern
- SPH conversion factor:
- A refined solid mesh with default SPH conversion factor 1 and a coarse solid mesh with factor of 3 does not converge although the number of SPH elements is similar
- A moderate solid mesh with SPH conversion factor of 2 provides accurate results with similar number of SPH elements
- SPH kernel:
- Enhanced kernel provided more accurate results as compared to classical formulation
- However, enhanced kernel can be run only with a single processor causing large simulation time
- Type of enhanced formulation:
- Out of quadratic, cubic and quintic, cubic formulation is most stable
- Linear viscosity:
- Linear viscosity needs to be scaled up to the order of 15 to get accurate results
FE model used in the SPH simulation consisted of 64800 C3D8R elements results in 589000 PC3D elements. Steel cover of 5mm thickness has been modeled using shell elements and general contact has been defined for particle and shell elements.
Results obtained from SPH simulation in comparison with test data and CEL is summarized in table below
|
|
Projectile tip X' (m) |
Projectile tip Y' (m) |
Path Length (m) |
X'-Y' Rest Angle (degrees) |
No. of CPUs |
Total CPU Time |
|
TEST |
0.62 |
0.69 |
0.93 |
43.00 |
- |
- |
|
CEL |
0.60 |
0.78 |
0.98 |
37.69 |
16 |
~ 11 Hrs |
|
SPH |
0.57 |
0.77 |
0.96 |
36.35 |
1 |
~ 98 Hrs |
As presented in above figure axial and lateral accelerations obtained from SPH simulation follow the general trend of acceleration plots obtained from CEL simulation and experimental data.
Manoj Chinnakonda, Jarek Konert, Huaning Zhu and Kedar Walvekar have been helpful with their valuable inputs and contribution to this study. Ashish Kulkarni has been actively involved in this work.
